I am unable to solve Gentleman Hat Dilemna , Problem Code : ALGO22001

link : Contest Page | CodeChef someone please give algo or solve in C++

hey @saumya220901 :wave:
This is a PNC (principle of inclusion and exclusion) based problem, In this you have to firstly find the no of combination of choosing 3 person among the n person, then by using principle of inclusion and exclusion find the total possible combination for each person not having their own cap.

My code in PYTHON :

fact=[1]*(50)
for i in range(1,41):
    fact[i]=fact[i-1]*i
n=int(input())
ans=0
tot=n*(n-1)*(n-2)//6
n-=3
for i in range(n+1):
    if i%2==0:
        ans+=(fact[n]//(fact[n-i]*fact[i]))*fact[n-i]
    else:
        ans-=(fact[n]//(fact[n-i]*fact[i]))*fact[n-i]
ans*=tot
print(ans)

You can use similar approch in c++ but using long long can lead to overflow so you can use a 128 bit int but not sure it will work as upper limit of n is not given so in value more than 34 it will overflow that too.